Linear Systems
June 12, 2012
Notes
1. The following are formulas predicting future raises for four different groups of union
employees. N represents the number of years from the start date of all the contracts. Each
equation represents the salary that will be earned after N years.
Group A: S  N   30,000  1,500N
Group B:
S  N   30,000  1,800N
Group C:
S  N   27,000  1,500N
Group D:
S  N   21,000  2,100N
a. Will group A ever earn more in a given year than group B? Explain.
b. Will group C ever catch up to group A? Explain.
c. Will group D ever catch up to group C? Explain.
d. If the answer in part c was yes, after how many years will it take for group D to catch up
to group C AND at what salary?
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Linear Systems
June 12, 2012
2. A small paint dealer has determined that the demand function for interior white paint is:
3q  4 p  240 ,
where p is the price of paint in dollars/gallon and q is the quantity of paint in gallons. Let q
be the independent variable and let p be the dependent variable.
a. Determine the vertical intercept.
p: price of paint in dollars per gallon
70
60
50
40
b. Determine the horizontal intercept.
30
20
10
10
20
30
40
50
q: number of gallons
60 70 80
c. Sketch the demand function.
d. Complete the following sentence:
The demand function says that a consumer is willing to buy more paint when…
e. The supply function for interior white paint is
p  0.85q
What price per gallon would suppliers be willing to sell the paint for if they supply
i.
0 gallons of paint
ii.
f.
80 gallons of paint
Sketch the supply function on the same graph as the demand function above.
g. Complete the following sentence:
The supply function says that a supplier is willing to sell more paint when…
h. Find the intersection point and interpret its meaning.
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Linear Systems
June 12, 2012
3. Tables & Chairs A small company manufactures unfinished tables and chairs. Each table
requires 3 hours of sawing and 1 hour of assembly. Each chair requires 2 hours of sawing
and 2 hours of assembly. The company is able to complete 12 hours of sawing and 8 hours
of assembly work each day. Find the number of tables and chairs the company can make
daily.
4. The student activities department of FLC plans to rent buses and vans for a spring break
trip. Each bus has 40 regular seats and 1 handicapped seat; each van has 8 regular seats
and 3 handicapped seats. There are 320 regular and 36 handicapped seats required for
this trip. How many of each type of transportation will be needed to meet these needs?
a. Define the variables of this situation.
b. Write the system of equations that represents this situation.
c. Solve the system of equations written in part b.
d. Interpret part c in the context of the problem.
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Linear Systems
June 12, 2012
5. Leslie is interested in buying a new car. She compares the cost of owning two cars she
likes:
Car A: An $18,000 gas-powered car that gets 20 mi/gal
Car B: A $22,800 hybrid-electric car that gets 50 mi/gal
**For this comparison, assume that the price of gas is $3 per gal.
a. Write a linear equation that models the cost, CA, of purchasing Car A as a function of the
miles driven, d. Use function notation.
b. Write a linear equation that models the cost, CB, of purchasing Car B as a function of the
miles driven, d. Use function notation.
c. Find the number of miles that Leslie needs to drive so that the cost of owning Car A is
the same as the cost of owning car B. Show all work.
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